NORTH ALLEGHENY SCHOOL DISTRICT
HONORS GEOMETRY SYLLABUS
COURSE NUMBER: 3201
Units of Credit: 1
Course Length: 184 days
Honors Geometry Syllabus
This is a rigorous course for students who had Advanced Algebra I in grades 6, 7, or 8. This is the second year of an honors mathematics sequence. In this course, students will develop reasoning and problem-solving skills in the areas of congruence, similarity, properties of lines, properties of triangles, properties of quadrilaterals, and properties of circles. The course will also include work with perimeter, area, circumference, surface area, and volume to solve real world problems. In addition to the geometry content, this course includes numerous examples and exercises involving algebra, data-analysis, and probability. Honors Geometry provides instruction and practice on standardized test questions in a variety of formats including multiple choice, short response, and extended response.
Mathematics Department Curriculum Differentiation
The Advanced/Honors Mathematics courses are intended to be more challenging than Academic courses and are designed to provide multiple opportunities for students to take an increased responsibility for their own learning and achievement. These courses are designed for students who have demonstrated an advanced level of achievement in mathematics. The curriculum is distinguished by a difference in rigor, relevance, and the quality of the work, not merely the quantity. The content of these courses is rigorous in its breadth and depth of study.
The key distinctions between Academic and Advanced/Honors curriculum at each level are:
- Expectation of Performance: Students in Advanced/Honors Mathematics courses will have different performance expectations.
- Assignments: The complex nature of Advanced/Honors Mathematics courses will have assignments that reflect the rigor of these courses.
- Pacing Guides: The pacing of instruction of the Advanced/Honors Mathematics courses will be accelerated to challenge the students enrolled in these courses.
- Assessments: The assessments of the Advanced/Honors Mathematics course will include cognitive and performance based tasks that will measure the students’ synthesis, application and analysis of the material.
Larson, Boswell, Geometry A Common Core Curriculum, Pennsylvania: Big Ideas Learning, 2015.
The following topics are covered in Honors Geometry:
Chapter 1: Basics of Geometry
- Name points, lines, planes, segments, and rays.
- Find segment lengths using Ruler Postulate, the Segment Addition Postulate, midpoints, segment bisectors, and the Distance Formula.
- Classify polygons and angles.
- Find perimeters and areas of polygons in the coordinate plane.
- Construct congruent segments and angles, and bisect segment and angles.
Chapter 2: Reasoning and Proof
- Write conditional and biconditional statements.
- Use inductive and deductive reasoning.
- Use properties of equality to justify the steps in solving equations and to find segment lengths and angle measures.
- Write two-column proofs, flowchart proofs, and paragraph proofs.
Chapter 3: Parallel and Perpendicular Lines
- Identify planes, pairs of angles formed by transversals, parallel lines, and perpendicular lines.
- Use properties and theorems of parallel lines.
- Prove theorems about parallel lines and about perpendicular lines.
- Write equations of parallel lines and perpendicular lines.
- Find the distance from a point to a line.
Chapter 4: Transformations
- Perform translations, reflections, rotations, dilations, and compositions of transformations.
- Solve real-life problems involving transformations.
- Identify lines of symmetry and rotational symmetry.
- Describe and perform congruence transformations and similarity transformations.
Chapter 5: Congruent Triangles
- Identify and use corresponding parts.
- Use theorems about the angles of a triangle.
- Use SAS, SSS, HL, ASA, and AAS to prove two triangles congruent.
- Prove constructions.
- Write coordinate proofs.
Chapter 6: Relationships Within Triangles
- Understand and use angle bisectors and perpendicular bisectors to find measures.
- Find and use the circumcenter, incenter, centroid, and orthocenter of a triangle.
- Use the Triangle Midsegment Theorem and Triangle Inequality Theorem.
- Write indirect proofs.
Chapter 7: Quadrilaterals and Other Polygons
- Find and use the interior and exterior angles of polygons.
- Use properties of parallelograms and special parallelograms.
- Prove that a quadrilateral is a parallelogram.
- Identify and use properties of trapezoids and kites.
Chapter 8: Similarity
- Use the AA, SSS, and SAS Similarity Theorems to prove triangles are similar.
- Decide whether polygons are similar.
- Use similarity criteria to solve problems about lengths, perimeters, and areas.
- Prove the slope criteria using similar triangles.
- Use the Triangle Proportionality Theorem and other proportionality theorems.
Chapter 9: Right Triangles and Trigonometry
- Use the Pythagorean Theorem and the Converse of the Pythagorean Theorem.
- Use geometric means.
- Find side lengths and solve real-life problems involving special right triangles.
- Find the tangent, sine, and cosine ratios and use them to solve real-life problems.
- Use the Law of Sines and Law of Cosines to solve triangles.
Chapter 10: Circles
- Identify chords, diameters, radii, secants, and tangents of circles.
- Find angle and arc measures.
- Use inscribed angles and polygons and circumscribed angles.
- Use properties of chords, tangents, and secants to solve problems.
- Write and graph equations of circles.
Chapter 11: Circumference, Area, and Volume
- Measure angles in radians
- Find arc lengths and areas of sectors of circles.
- Find areas of rhombuses, kites, and regular polygons.
- Find and use volumes of prisms, cylinders, pyramids, cones, and spheres.
- Describe cross-sections and solids of revolution.
Expected Levels of Student Achievement
Course grades will be determined by the collective point totals from assessments, homework, classroom projects/participation and standardized test preparation assignments. It is expected that all students will participate in daily classroom activities and maintain a notebook. Students must complete all assigned work and participate in class discussion.
Students are expected to continue to grow in their use of technology. Students are expected to obtain a graphics calculator. We recommend purchasing from the Texas Instruments TI-84 family of calculators. Students are expected to access online resources, www.bigideas.com, and grades.
Standard Test Preparation
The North Allegheny Mathematics Curriculum is designed to prepare students for standardized tests while meeting PA Core Standards and Eligible Content for Mathematics. The focus will be on numbers and operations, algebraic concepts, geometry, data analysis and probability, and measurement. Students will be expected to complete real-life problem solving tasks throughout the course.
Pre-Requisites for Next Course
Students having completed Honors Geometry, must have earned a 80% or better in order to advance to Honors Algebra 2.